Locally maximal homoclinic classes for generic diffeomorphisms

نویسنده

  • Manseob Lee
چکیده

Let M be a closed smooth d(≥ 2) dimensional Riemannian 1 manifold and let f : M → M be a diffeomorphism. For C generic f , a 2 locally maximal homogeneous homoclinic class is hyperbolic. 3 M.S.C. 2010: 37C20; 37D20. 4

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Applications of Mañé’s C Connecting Lemma

We consider a few applications of Mañé’s C2 Connecting Lemma. These are the C2 creation of homoclinic points associated to a basic set (i.e., isolated transitive hyperbolic set), a C2 locally generic criterion to know whether a given point belongs to the stable set of hyperbolic homoclinic classes, and that measurably hyperbolic diffeomorphisms (i.e., having the closure of supports of all invar...

متن کامل

Expansive homoclinic classes

We prove that for C generic diffeomorphisms, every expansive homoclinic class is hyperbolic.

متن کامل

Generic Bi-lyapunov Stable Homoclinic Classes

We study, for C generic diffeomorphisms, homoclinic classes which are Lyapunov stable both for backward and forward iterations. We prove they must admit a dominated splitting and show that under some hypothesis they must be the whole manifold. As a consequence of our results we also prove that in dimension 2 the class must be the whole manifold and in dimension 3, these classes must have nonemp...

متن کامل

Abundance of C-robust homoclinic tangencies

A diffeomorphism f has a C-robust homoclinic tangency if there is a C-neighbourhood U of f such that every diffeomorphism in g ∈ U has a hyperbolic set Λg, depending continuously on g, such that the stable and unstable manifolds of Λg have some non-transverse intersection. For every manifold of dimension greater than or equal to three, we exhibit a local mechanism (blender-horseshoes) generatin...

متن کامل

The Entropy Conjecture for Diffeomorphisms Away from Tangencies

We prove that every C1 diffeomorphism away from homoclinic tangencies is entropy expansive, with locally uniform expansivity constant. Consequently, such diffeomorphisms satisfy Shub’s entropy conjecture: the entropy is bounded from below by the spectral radius in homology. Moreover, they admit principal symbolic extensions, and the topological entropy and metrical entropy vary continuously wit...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2017